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Concept explainers
a.
Construct the frequency distribution with a class width of 5 and a lower limit of 45 for the first class.
a.
![Check Mark](/static/check-mark.png)
Answer to Problem 10RE
The frequency distribution is,
Age | Frequency |
45-49 | 2 |
50-54 | 1 |
55-59 | 4 |
60-64 | 6 |
65-69 | 6 |
70-74 | 6 |
75-79 | 4 |
80-84 | 3 |
85-89 | 2 |
90-94 | 4 |
Total | 38 |
Explanation of Solution
Calculation:
The given information is that a data representing the age at which the all U.S. presidents died.
Frequency:
The frequencies are calculated by using the tally mark and the
- Based on the given information, the class intervals are 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75-79, 80-84, 85-89, 90-94.
- Make a tally mark for each value in the corresponding age class and continue for all values in the data.
- The number of tally marks in each class represents the frequency, f of that class.
Similarly, the frequency of remaining classes for the age is given below:
Age | Tally | Frequency |
45-49 | 2 | |
50-54 | 1 | |
55-59 | 4 | |
60-64 | 6 | |
65-69 | 6 | |
70-74 | 6 | |
75-79 | 4 | |
80-84 | 3 | |
85-89 | 2 | |
90-94 | 4 | |
Total | 38 |
b.
Construct the frequency histogram based on the frequency distribution.
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 10RE
Output obtained from MINITAB software for the ages is:
Explanation of Solution
Calculation:
Frequency Histogram:
Software procedure:
- Step by step procedure to draw the frequency histogram for the ages using MINITAB software.
- Choose Graph > Bar Chart.
- From Bars represent, choose unique values from table.
- Choose Simple.
- Click OK.
- In Graph variables, enter the column of Frequency.
- In Categorical variables, enter the column of Ages.
- Click OK
- Select Edit Scale, Enter 0 in Gap between clusters.
Observation:
From the bar graph, it can be seen that maximum age at death for the U.S. presidents is in the interval 60-75.
c.
Construct a relative frequency distribution for the data.
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 10RE
The relative frequency distribution for the data is:
Age | Relative frequency |
45-49 | 0.053 |
50-54 | 0.026 |
55-59 | 0.105 |
60-64 | 0.158 |
65-69 | 0.158 |
70-74 | 0.158 |
75-79 | 0.105 |
80-84 | 0.079 |
85-89 | 0.053 |
90-94 | 0.105 |
Explanation of Solution
Calculation:
Relative frequency:
The general formula for the relative frequency is,
Therefore,
Similarly, the relative frequencies for the remaining ages are obtained below:
Age | Frequency | Relative frequency |
45-49 | 2 | |
50-54 | 1 | |
55-59 | 4 | |
60-64 | 6 | |
65-69 | 6 | |
70-74 | 6 | |
75-79 | 4 | |
80-84 | 3 | |
85-89 | 2 | |
90-94 | 4 | |
Total | 38 |
d.
Construct the relative frequency histogram based on the frequency distribution.
d.
![Check Mark](/static/check-mark.png)
Answer to Problem 10RE
Output obtained from MINITAB software for the ages is:
Explanation of Solution
Calculation:
Relative Frequency Histogram:
Software procedure:
- Step by step procedure to draw the relative frequency histogram for the ages using MINITAB software.
- Choose Graph > Bar Chart.
- From Bars represent, choose unique values from table.
- Choose Simple.
- Click OK.
- In Graph variables, enter the column of Relative Frequency.
- In Categorical variables, enter the column of Ages.
- Click OK
- Select Edit Scale, Enter 0 in Gap between clusters.
Observation:
From the bar graph, it can be seen that maximum age at death for the U.S. presidents is in the interval 60-75.
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Chapter 2 Solutions
Essential Statistics
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